Respuesta :
Given:
The given equation is
[tex]x^2-8x+16=0[/tex]
To find:
The correct statement for the given equation.
Solution:
We have,
[tex]x^2-8x+16=0[/tex]
It can be written as
[tex]x^2-2(x)(4)+(4)^2=0[/tex]
Using the identity of perfect square trinomial, we get
[tex](x-4)^2=0[/tex] [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]
[tex](x-4)=0[/tex]
[tex]x=4[/tex]
Here, x=4 has multiplicity two because the power of factor (x-4) is 2.
x=4 is a double root and the equation is a perfect trinomial.
Therefore, the correct options are C and E.
Answer:
B) Factor to solve.
C) x = 4 is a double root.
E) The equation is a perfect square trinomial.
Step-by-step explanation:
Factor to solve.<
By inspection, the equation is a perfect square trinomial.
x = 4 is a double root
By inspection, the middle term's coefficient 8 is twice the square root of 16, the constant; therefore, it is a perfect square trinomial.
x2 − 8x + 16 = 0 → (x − 4)(x − 4) = 0 → x = 4 is a double root.
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